SCIO is an antiferromagnetic insulator, 0.50-0.57 eV per simulation cell more favorable than the ferromagnetic phase. The AFM configuration comprises mixed Co, Ir planes that couple antiparallel along the [110]-direction, as can be seen from the spin density plotted in Fig. REF (g)-(i). This configuration was found to be more stable than AFM order along the [111] or [001]-directions in preliminary calculations[1]} with the WIEN2k code [2]}, and is consistent with the magnetic order determined from neutron powder diffraction. [3]}. The spin moment of Co in SCIO (\(\sim 2.74\)  \(\mu _{\rm B}\) ) is comparable to the one in bulk SCO [2.51 \(\mu _{\rm B}\)  (FM) and 2.85 \(\mu _{\rm B}\)  (AFM)] and close to the experimental (2.6(1) \(\mu _{\rm B}\) ) and theoretical value (\(\sim 3.00\)  \(\mu _{\rm B}\) ) reported in Ref. [3]}. Most interestingly, Ir acquires a significant magnetic moment of \(1.31-1.38\)  \(\mu _{\rm B}\) , compared to the zero magnetic moment in bulk SIO and at variance with a vanishing contribution of Ir suggested from experiment [3]} (the theoretical value from that study is \(\sim 0.81\)  \(\mu _{\rm B}\) ). The origin of this effect will be discussed in the next subsection. Including SOC, the spin moments of both ions are somewhat reduced and show a weak dependence on strain: 2.35-2.45 \(\mu _{\rm B}\)  for Co and 1.21-1.25 \(\mu _{\rm B}\)  for Ir with increasing lateral lattice constant. At the same time the orbital moments are substantially enhanced w.r.t. the end members and vary between 0.31-0.46 \(\mu _{\rm B}\)  for Co (the latter at \(a_{\rm STO}\) ) and 0.14-0.13 \(\mu _{\rm B}\)  for Ir. Recent XAS measurements [6]} suggest a switching of the magnetic easy axis. While our results do not show a reversal, the energy difference between the preferred [100]-magnetization direction over the [001] decreases from 85 meV to 70 meV per 40-atom u.c. from compressive to tensile strain.
